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Convergence and stability of two classes of theta-Milstein schemes for stochastic differential equations.
- Source :
-
Journal of Computational & Applied Mathematics . Jul2018, Vol. 336, p8-29. 22p. - Publication Year :
- 2018
-
Abstract
- This paper examines convergence and stability of the two classes of theta-Milstein schemes for stochastic differential equations (SDEs) with non-global Lipschitz continuous coefficients: the split-step theta-Milstein (SSTM) scheme and the stochastic theta-Milstein (STM) scheme. For θ ∈ [ 1 ∕ 2 , 1 ] , this paper concludes that the two classes of theta-Milstein schemes converge strongly to the exact solution with the order 1. For θ ∈ [ 0 , 1 ∕ 2 ] , under the additional linear growth condition for the drift coefficient, these two classes of the theta-Milstein schemes are also strongly convergent with the standard order. This paper also investigates exponential mean-square stability of these two classes of the theta-Milstein schemes. For θ ∈ ( 1 ∕ 2 , 1 ] , these two theta-Milstein schemes can share the exponential mean-square stability of the exact solution. For θ ∈ [ 0 , 1 ∕ 2 ] , similar to the convergence, under the additional linear growth condition, these two theta-Milstein schemes can also reproduce the exponential mean-square stability of the exact solution. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 336
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 127842508
- Full Text :
- https://doi.org/10.1016/j.cam.2017.12.025